Answer

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**Hint:**We are asked to find the average of a set of numbers. The average of a set of numbers is the number between the largest and the smallest number in the set. It is defined as the ratio of the sum of all the values in a set of numbers to the total number of values.

**Complete step-by-step answer:**

We are asked to find the average of a set of numbers. We will be solving the given question using the concept of statistics.

The average value of the set of numbers is the middle value or the central value in the set. It is calculated by dividing the sum of the values in the given set by the total number of values.

Writing the above lines in the form of the equation, we get,

$\Rightarrow \text{Average = }\dfrac{\text{sum of all the terms}}{\text{total number of terms}}$

Let us understand the concept of finding the average of a set of numbers through an example.

Example: Find the average of the numbers 13, 45, 67, 32, and 31.

From the above, we know that

$\Rightarrow \text{Average = }\dfrac{\text{sum of all the terms}}{\text{total number of terms}}$

We need to find the sum of all the terms and the total number of terms to calculate the average for the given set of numbers.

The given numbers are 13, 45, 67, 32, and 31. So, the total number of terms is 5.

Writing the above line in the form of the equation, we get,

$\therefore \text{total number of terms = 5}$

Now, we need to find the sum of all the numbers.

Finding the sum of all the given numbers, we get,

$\Rightarrow \text{sum of all terms = }13+45+67+32+31$

Simplifying the above equation, we get,

$\therefore \text{sum of all terms = }188$

Substituting the values in the formula, we get,

$\Rightarrow \text{Average = }\dfrac{188}{5}$

Simplifying the above expression, we get,

$\therefore \text{Average = 37}\text{.6}$

**Note:**For any set of numbers, we must always remember that the value of the average is always greater than the smallest number in the set and is lesser than the largest number in the set. We must be careful while performing arithmetic operations to get precise results.

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